I've messed around with PvP in 4e a little bit and I've found that one of the most important aspects is controlling the economy of action. That is to say you want to maximize your potential actions while at the same time minimizing your opponents.
The first thing you have to consider is that you may not get to go first, which means you have to be able to survive a nova or a debilitating condition out of the gate. An interrupt that prevents additional attacks by moving you out of range or the like is best for the former, and a force miss is better for the latter.
You can control your opponents economy of action with:
Nova breaks (i.e. things that cause multi hit attacks to fail)
Force misses
Status effects (Things like stun and daze an effectively prevent melee from hitting your and forces range to choose between attacking and putting space between you, as well as taking away their ability to use interrupts to foil you, eye bite's another good example of this or dominating them and getting rid of their weapon/implement.)
Controlling space and movement (melee that can't close or range that can't get breathing room loses effectiveness. If you force someone to close to hit you, then they can't use their move to get away from you)
Healing (most healing is a minor action, if you survive an attack you can effectively undo it with a lower cost in action that it took to make it in the first place, if you've caused them to use up their burst damage resources healing becomes more effective.)
You can increase your action efficiency with:
multi-attacks (Be wise and set yourself up, try to put your opponent in a position that they can't interrupt it, either by forcing them to use up those resources or making them unable to use them. Try to increase your likely hood of hitting. Don't use the power until you have a good chance of killing them with it, if they don't die they could undo all your work very quickly. Also stack bonuses to damage are very good here. This is controllable burst, unlike crits.)
accuracy (a miss is pretty much as good as doing nothing, increase bonuses, accrue rerolls, go after bad defenses. Hits force your opponent to use resources, misses do little to nothing.)
automatic damage
I'm sure I've forgotten to mention some things, but in short prevent, reduce the effectiveness, or undo your opponents actions while at the same time trying to stop him from doing the same to you.
[edit: You'll notice I didn't recommend a class or build, that's because I don't believe there is a clear cut winner. While there are some classes that are better suited for this than others, a lot of it is choosing the right tools and using them effectively. So choose a path to victory and build to support it.]